Radu Laza Professor Department of Mathematics Stony Brook University

Office: Math 4-121

E-mail: radu.laza@stonybrook.edu

Teaching

• Spring 2023 -- MAT 589 (Intro to Algebraic Geometry)
• Fall 2022 -- MAT 211 (Intro to Linear Algebra), MAT 312/AMS 351 (Applied Algebra)

Recent & Selected Publications:

• Deformations of Calabi-Yau varieties with k-liminal singularities (w. R. Friedman), preprint 2023.
• The Higher Du Bois and higher rational singularities properties for isolated singularities (w. R. Friedman), preprint 2022.
• Higher Du Bois and higher rational singularities (w. R. Friedman, and an Appendix by M. Saito), preprint 2022.
• Non-isomorphic smooth compactifications of the moduli space of cubic surfaces (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), preprint 2022.
• Deformations of some local Calabi-Yau manifolds (w. R. Friedman), preprint 2022.
• Deformations of singular Fano and Calabi-Yau varieties (w. R. Friedman), preprint 2022.
• Hodge theory of degenerations, (II): Vanishing cohomology and geometric applications, (w. M. Kerr), preprint 2020.
• Period mappings and ampleness of the Hodge bundle, (w. M. Green, P. Griffiths, and C. Robles), preprint 2020.
• Cohomology of the moduli space of cubic threefolds and its smooth models (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), Mem. Amer. Math. Soc. 282 (2023), No. 1391.
• Smoothing of rational singularities and Hodge structure (w. M. Kerr and M. Saito), Algebr. Geom. 9 (4) (2022) 476-501.
• The LLV decomposition of hyper-Kaehler cohomology (w. M. Green, YJ Kim, and C. Robles), Math. Ann. 382 (2022), no. 3-4, 1517-1590
• Automorphisms and Periods of Cubic Fourfolds (with Z. Zheng), Math. Z. 300 (2022), no. 2, 1455-1507.
• Hodge theory of degenerations, (I): Consequences of the decomposition theorem , (w. M. Kerr; with an Appendix by M. Saito), Selecta Math. 27 (2021), No. 4, Paper No. 71.
• Maximally algebraic potentially irrational cubic fourfolds, Proc. Amer. Math. Soc. 149 (2021), no. 8, 3209-3220.
• GIT versus Baily-Borel compactification for K3's which are double covers of P1xP1 (w. K. O'Grady), Adv. Math. 383 (2021), Paper No. 107680.
• Complete moduli of cubic threefolds and their intermediate Jacobians (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), Proc. Lond. Math. Soc. 122 (2021), no. 2, 259-316.
• A conjectural bound on the second Betti number for hyper-Kaehler manifolds (w. YJ Kim), Bull. Soc. Math. France 148 (2020), no. 3, 467-480.
• The Euler number of hyper-Kaehler manifolds of OG10 type (w. K. Hulek and G. Sacca), in Proceedings of the ICM 2018 Satellite conference "Moduli Spaces in Algebraic Geometry and Applications", Mat. Contemp. 47 (2020), 152-172.
• Birational geometry of the moduli space of quartic K3 surfaces, (with K. O'Grady), Compositio Math. 155 (2019), no. 9, 1655-1710.
• On the moduli space of pairs consisting of a cubic threefold and a hyperplane, (w. G. Pearlstein and Z. Zhang), Adv. Math. 340 (2018), 684-722.
• Remarks on degenerations of hyper-Kaehler manifolds, (with J. Kollár, G. Saccà and C. Voisin), Ann. Inst. Fourier (Grenoble) 68 (2018), no. 7, 2837-2882.
• GIT versus Baily-Borel compactification for quartic K3 surfaces, (with K. O'Grady), in "Geometry of Moduli" (Abel Symposia), Springer, 2018, 217-283.
• A hyper-Kaehler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold (with G. Saccà and C. Voisin), Acta Math. 218 (2017), no. 1, 55-135.
• Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), J. Eur. Math. Soc 19 (2017), no. 3, 659-723.
• The KSBA compactification for the moduli space of degree two K3 pairs, J. Eur. Math. Soc. 18 (2016), no. 2, 225-279.
• Log canonical models and variation of GIT for genus four canonical curves (w. S. Casalaina-Martin and D. Jensen), J. Algebraic Geom. 23 (2014), 727-764.
• Semi-algebraic horizontal subvarieties of Calabi-Yau type (w. R. Friedman), Duke Math. J. 162 (2013), no. 12, 2077-2148.
• Simultaneous semi-stable reduction for curves with ADE singularities (w. S. Casalaina-Martin), Trans. Amer. Math. Soc. 365 (2013), no. 5, 2271-2295.
• Moduli space of cubic fourfolds via the period map, Ann. of Math. 172 (2010), no. 1, 673-711.
• Moduli space of cubic fourfolds (the GIT compactification), J. Algebraic Geom. 18 (2009), 511-545.
• The moduli space of cubic threefolds via degenerations of the intermediate Jacobian (w. S. Casalaina-Martin), J. Reine Angew. Math. 633 (2009), 29-65.

Expository:

• Classical Period Domains (with Z. Zhang), in Recent Advances in Hodge Theory (London Mathematical Society Lecture Note Series), Cambridge Univ. Press, 2016.
• Perspectives on the construction and compactification of moduli spaces, in Compactifying Moduli Spaces (Advanced Courses in Mathematics, CRM Barcelona), Birkhauser, 2016, 1-35.
• GIT and moduli with a twist, in "Handbook of Moduli" vol. 2, Adv. Lect. Math. 25 (2013), Int. Press, 259-297.

Books edited:

• Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses (w. Schuett and N. Yui), lecture notes based on the concentrated graduate courses held during the thematic program on Calabi-Yau varieties at Fields Institute (Fall 2013), Fields Institute Monographs, Springer 2015.
• Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds (w. M. Schuett and N. Yui), Fields Institute Communications, vol. 67, Springer 2013, (Proceedings of the 2011 Fields workshop on Calabi-Yau's and K3's).

My papers on arXiv. My Scholar profile.

My research is partially supported by NSF (DMS-2101640).

• Singularities and Algebraic Geometry (Vietnam, February 2023)
• Explicit moduli problems in higher dimensions (Banff, March 2023)
• The Georgia Algebraic Geometry Symposium (UGA, April 2023)
• ANT seminar at U. Arizona (May 2023)
• Valley Geometry Seminar (May 2023)